Chart for estimating tournament returns

[allenciox]

Ok, I have put together a chart for measuring tournament returns for quick tournaments, based on your team's probability of winning a game against an average team in each type of tournament.

win	#		prob of	PP 	#
prob	teams	format	winning	return	games

40%	8	DoD	6.4%	13	1.56
	16	RRF3	2.0%	57	3.31
	16	bo3	1.5%	44	4.03
	16	bo5	1.0%	29	6.22
	32	DRRF3	0.7%	43	3.84
	32	bo7	0.2%	12	8.56
50%	8	DoD	12.5%	25	1.75
	16	RRF3	6.3%	178	3.81
	16	bo3	6.3%	178	5.06
	16	bo5	6.3%	178	8.14
	32	DRRF3	3.1%	191	4.66
	32	bo7	3.1%	191	12.09
60%	8	DoD	21.6%	43	1.96
	16	RRF3	15.1%	431	4.44
	16	bo3	17.6%	503	6.4
	16	bo5	21.7%	619	10.76
	32	DRRF3	9.8%	598	5.7
	32	bo7	18.1%	1102	17.83

Now to explain. Suppose you expect your team is overmatched in the tournaments, and you only expect that you can win about 40% of your games, on average.

So if you enter an 8-team DOD tournament, then you have a 6.4% chance of winning the tournament (about half that of an average team) and you can expect to earn, on average, about 13 PP (this assumes a standard pack is worth 950 PP). On average, your team will make it through a bit over 1.5 games, or sims. So if you do lose, you can enter another tourney quickly.

On the other hand, if that same team enters a 32 team bo7 tourney, then it will win the tourney only two times out of a thousand (pretty amazing!). The average PP return in that case is only slightly less, at 12, but you have to wait for an average of more than 8.5 games (sims) before losing.

How much different it is for a team that can win 60% of its games! In that case, the DoD tourney would return 43 pp on average. However, the 32-team b07 tourney would return 1102 PP on average, for an average investment of about 18 sims (i.e. three hours).

One interesting case to look at here is comparing the 60% player in 16-team b05 tourney vs. 32-team b07 tourney. In this case, the probability of winning only drops from 22% to 18% (almost six times greater than the average player) even though twice as many people are competing. The time invested does increase about 65% between the two, but the 32-team bo7 tourney returns almost twice as much. So it is pretty close to a wash.

These are all based on the new tourney pay structure, which actually encourages RRF3 and DRRF3 for average players as the payout is the same for the b05 or b07 but requires much less time investment. The real sweet spot for the 40% and 50% game winner is clearly the 16-team RRF3 tournament.

[Barmy Fungy-Phipps]

Appreciate the work! I'd done the easy calculations in my head, but it's good to have the more complex stuff spelled out.

I was thinking about the longer tournaments, and I think the odds are a bit tougher than in your calculations. If we assume an even distribution of team strength (let's say roughly 1/3 each of 40%, 50%, and 60% in likelihood to win), there will be a slight increase in difficulty every round. Two 60% teams facing each other no longer have their prior advantage, and a 40% is even more likely to get knocked out.

That corresponds pretty well with my experiences - I ran a lot of 8 team bronzes, and my win rate was over 20%, suggesting I had a slight advantage in team composition. I don't have nearly as many 32/bo7, but it is quite a few, and my win rate is a lot closer to 3% than 18%. It is a slightly different roster, but I've checked my team against overall performance, and I'm still fielding about a good a bronze team as is possible. I think after the first 2/3 rounds, the longer tournaments are back to even odds, at best.

[allenciox]

Originally Posted by Barmy Fungy-Phipps

Appreciate the work! I'd done the easy calculations in my head, but it's good to have the more complex stuff spelled out.

I was thinking about the longer tournaments, and I think the odds are a bit tougher than in your calculations. If we assume an even distribution of team strength (let's say roughly 1/3 each of 40%, 50%, and 60% in likelihood to win), there will be a slight increase in difficulty every round. Two 60% teams facing each other no longer have their prior advantage, and a 40% is even more likely to get knocked out.

That corresponds pretty well with my experiences - I ran a lot of 8 team bronzes, and my win rate was over 20%, suggesting I had a slight advantage in team composition. I don't have nearly as many 32/bo7, but it is quite a few, and my win rate is a lot closer to 3% than 18%. It is a slightly different roster, but I've checked my team against overall performance, and I'm still fielding about a good a bronze team as is possible. I think after the first 2/3 rounds, the longer tournaments are back to even odds, at best.

Agree completely with your analysis... in the analysis I did, the opponent you have is random, which is a simplified case. To do the full analysis is much more complex: you obviously face, on average, better opponents in later rounds than earlier rounds. So this is an approximation only.

An alternative would be to set up 16, 32, etc. teams so that they each have a random distribution from 35% winners to 65% winners, and use log5 to calculate probabilities of each game through tournament. Then run millions of simulated tournaments. I am considering doing that this weekend and seeing how results differ.

[Barmy Fungy-Phipps]

Awesome idea. That's a good step beyond my experience level, but I'm very interested seeing the results.

[neugey]

(Jim Carrey voice) "So you're saying there's still a chance?"